Logo
ScienceStack
Table of Contents
Fetching ...
Sign In

Distributed Model Predictive Covariance Steering

Augustinos D. Saravanos, Isin M. Balci, Efstathios Bakolas, Evangelos A. Theodorou

TL;DR

DiMPCS addresses safe and scalable control for large teams of robots under stochastic disturbances by integrating covariance steering with Wasserstein-distance distribution matching into a distributed MPC framework. It linearizes nonlinear dynamics, employs disturbance-feedback policies, and transforms probabilistic safety constraints into convex or quadratic forms, enabling decentralized ADMM-based optimization with local copy variables and consensus. The method supports receding-horizon execution and neighborhood-based communication, and is validated through extensive simulations (up to hundreds of robots) and hardware experiments on the Robotarium, showing favorable scalability and safety performance compared with other SMPC approaches. The combination of Wasserstein-based distribution steering, ADMM consensus, and MPC provides a practical, scalable approach for real-world multi-robot navigation under uncertainty.

Abstract

This paper proposes Distributed Model Predictive Covariance Steering (DiMPCS) for multi-agent control under stochastic uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single framework that is safe, scalable and decentralized. Initially, we pose a problem formulation that uses the Wasserstein distance to steer the state distributions of a multi-agent system to desired targets, and probabilistic constraints to ensure safety. We then transform this problem into a finite-dimensional optimization one by utilizing a disturbance feedback policy parametrization for covariance steering and a tractable approximation of the safety constraints. To solve the latter problem, we derive a decentralized consensus-based algorithm using the Alternating Direction Method of Multipliers. This method is then extended to a receding horizon form, which yields the proposed DiMPCS algorithm. Simulation experiments on a variety of multi-robot tasks with up to hundreds of robots demonstrate the effectiveness of DiMPCS. The superior scalability and performance of the proposed method is also highlighted through a comparison against related stochastic MPC approaches. Finally, hardware results on a multi-robot platform also verify the applicability of DiMPCS on real systems. A video with all results is available in https://youtu.be/tzWqOzuj2kQ.

Distributed Model Predictive Covariance Steering

TL;DR

DiMPCS addresses safe and scalable control for large teams of robots under stochastic disturbances by integrating covariance steering with Wasserstein-distance distribution matching into a distributed MPC framework. It linearizes nonlinear dynamics, employs disturbance-feedback policies, and transforms probabilistic safety constraints into convex or quadratic forms, enabling decentralized ADMM-based optimization with local copy variables and consensus. The method supports receding-horizon execution and neighborhood-based communication, and is validated through extensive simulations (up to hundreds of robots) and hardware experiments on the Robotarium, showing favorable scalability and safety performance compared with other SMPC approaches. The combination of Wasserstein-based distribution steering, ADMM consensus, and MPC provides a practical, scalable approach for real-world multi-robot navigation under uncertainty.

Abstract

This paper proposes Distributed Model Predictive Covariance Steering (DiMPCS) for multi-agent control under stochastic uncertainty. The scope of our approach is to blend covariance steering theory, distributed optimization and model predictive control (MPC) into a single framework that is safe, scalable and decentralized. Initially, we pose a problem formulation that uses the Wasserstein distance to steer the state distributions of a multi-agent system to desired targets, and probabilistic constraints to ensure safety. We then transform this problem into a finite-dimensional optimization one by utilizing a disturbance feedback policy parametrization for covariance steering and a tractable approximation of the safety constraints. To solve the latter problem, we derive a decentralized consensus-based algorithm using the Alternating Direction Method of Multipliers. This method is then extended to a receding horizon form, which yields the proposed DiMPCS algorithm. Simulation experiments on a variety of multi-robot tasks with up to hundreds of robots demonstrate the effectiveness of DiMPCS. The superior scalability and performance of the proposed method is also highlighted through a comparison against related stochastic MPC approaches. Finally, hardware results on a multi-robot platform also verify the applicability of DiMPCS on real systems. A video with all results is available in https://youtu.be/tzWqOzuj2kQ.
Paper Structure (20 sections, 1 theorem, 29 equations, 6 figures, 2 tables)

This paper contains 20 sections, 1 theorem, 29 equations, 6 figures, 2 tables.

Table of Contents

  1. INTRODUCTION
  2. Problem Description
  3. Notation
  4. Problem Description
  5. Multi-Agent Covariance Steering With Wasserstein Distance
  6. Dynamics Linearization
  7. Controller Parametrization
  8. State Mean and Covariance Expressions
  9. Problem Transformation
  10. Distributed Approach with ADMM
  11. Decentralized Consensus Approach
  12. Distributed Covariance Steering with Wasserstein Metric
  13. Distributed Model Predictive Covariance Steering
  14. Simulation Experiments
  15. Small-Scale Tasks
  16. ...and 5 more sections

Key Result

Proposition 1

The constraint control chance constraint can be equivalently expressed as with $a_{i,n} = \eta_{i,n}^{\mathrm {T}} {\bf S}_{i,k} \bar{{\bm u}}_i - \gamma_{i,n} + \bar{\beta} \lVert \eta_{i,n}^{\mathrm {T}} {\bf S}_{i,k} [{\bf L}_i, {\bf K}_i] {\bm \Psi}_i \rVert_2$ and ${\bm \Psi}_i = {\mathrm {bdiag}}(\Sigma_{i,0}^{1/2}, {\bf W}_i)$.

Figures (6)

  • Figure 1: Sixteen unicycle robots safely guided with DiMPCS to their target distributions while avoiding collisions.
  • Figure 2: A task with $16$ robots that must reach a target distribution at a diametrically opposite location while avoiding collisions. Each snapshot shows their positions and the $(\mu \pm 3 \sigma)$ confidence regions of planned distribution trajectories. The target distributions are shown as dashed ellipses with "x" at the center.
  • Figure 3: A task with $25$ robots required to pass through a narrow bottleneck before reaching their targets.
  • Figure 4: A large-scale task with 256 robots.
  • Figure 5: Hardware experiment with three robots that are required to reach their targets while avoiding collisions.
  • ...and 1 more figures

Theorems & Definitions (6)

  • Proposition 1
  • proof
  • Remark 1
  • Remark 2
  • Remark 3
  • Remark 4